Compute the one-dimensional discrete Fourier Transform.
This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT].
Parameters : | a : array_like
n : int, optional
axis : int, optional
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Returns : | out : complex ndarray
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Raises : | IndexError :
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See also
Notes
FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes.
The DFT is defined, with the conventions used in this implementation, in the documentation for the numpy.fft module.
References
[CT] | Cooley, James W., and John W. Tukey, 1965, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19: 297-301. |
Examples